Fractal Symmetric Phases of Matter

Understand

We study spin systems which exhibit symmetries that act on a fractal subset of sites, with fractal structures generated by linear cellular automata.

• In addition to the trivial symmetric paramagnet and spontaneously symmetry broken phases, we construct additional fractal symmetry protected topological (FSPT) phases via a decorated defect approach.
• Such phases have edges along which fractal symmetries are realized projectively, leading to a symmetry protected degeneracy along the edge.
• Isolated excitations above the ground state are symmetry protected fractons, which cannot be moved without breaking the symmetry.